3 Answers
3

Let me give a more detailed back-of-the-envelope approximation, which might actually be able to decide, given the conditions of the problem, if we would be able to hear the sound of Sun.

Assumptions:

The space between Earth and Sun is filled with uniform air. This is a non-physical assumption. It basically means we are ignoring the gravitational effects of both Sun and Earth; but then one should ask what keeps Sun and Earth from exploding into the space. Anyway, the question doesn't make much sense without this assumption. So, the space is filled with air at $1_{atm}$ pressure(ask the OP how :)

For comparison purposes, the minimum level of a pure tone at 1000 Hz has been standardized at a sound pressure of 20 micropascals. It is approximately the quietest sound a young healthy human can detect.

Looking at some typical minimum audibility curves, one sees that the above standard limit is actually really close to the global minimum(dB is a logarithmic scale of intensity itself, so I'm being a little bit sloppy here. But at the end of my calculations, I hope a small constant coefficient won't matter much).

Sound intensity $\propto$ (amplitude)$^2 \propto (\Delta P)^2$

Some amount of spherical symmetry.

Calculations:

I believe Sun is capable of creating pressure differences much higher than this, so one expects to hear Sun's noise loud and clear. One should be able to estimate typical pressure differences by looking at solar wind data.

But How loud is sun?

In order to estimate how loud sun is, we would have to concentrate on different things that might happen on Sun. A typical aspect which might be interesting are solar flares. Let's try and estimate the sound of a solar flare on earth. According to wikipedia:

A solar flare is a sudden brightening observed over the Sun's surface or the solar limb, which is interpreted as a large energy release of up to 6 × 1025 joules of energy (about a sixth of the total energy output of the Sun each second or 160,000,000,000 megatons of TNT equivalent, over 25,000 times more energy than released from the impact of Comet Shoemaker–Levy 9 with Jupiter).

So the intensity of a solar flare sound on Earth can be approximated with $1/6$ of solar constant $\approx 227_ \frac{W}{m^2}$. I have no idea how it will actually sound, but believe me that is well above a generic human's minimum hearing capability.

Sound, in simple words is vibration of air. So in theory yes, we should hear the Sun if there was a medium like air that could transfer the vibrations. That's just my opinion, of course I can be wrong as this is purely theoretical question and answer.

If this was a question of sound spreading with an inverse square law, the answer would be yes.

Place a cymbal at a distance where it has the same apparent diameter as the sun. On a quiet day, it would be audible. Place 4 cymbals at twice the distance. It would be just as loud.

Repeat this idea at the distance of the sun. If the average cymbal-sized patch of the sun's surface is louder than a cymbal, you should be able to hear the sun on Earth. Given the sun's atmosphere is full of shock waves and other violent events (See this paper), it sounds likely we could hear it.

But this isn't the full story. Air absorbs sound. The absorption coefficient is small, but the distance is $10^8$ miles or $1.5 * 10^{11}$ meters in round numbers. It would take 16 years for sound to reach the Earth.

Here is a calculator for atmospheric absorption. Absorption is lowest at low temperature, low humitidy, and low frequency. Under the best conditions conditions, it is about $10^-3$ dB/m. The intensity would be reduced by $1.5 * 10^{8}$ dB. So not even if we were downwind...

This post has a helioseismology link that shows sound waves travel from one side of the sun to the other with very large amplitudes. But this isn't the same thing. These are more like earthquakes than audible sound. And the sun is a power source that keeps them going.